A periodic orbit formula for quantum reactions through transition states

TL;DR

This paper derives a formula expressing quantum reaction probabilities as a sum over periodic orbits within the transition state, linking classical periodic dynamics with quantum reaction rates.

Contribution

It introduces a novel periodic orbit formula for quantum reactions through transition states, extending classical phase space methods to quantum computations.

Findings

Derived an absolutely convergent sum over periodic orbits for quantum reaction probabilities.

Connected classical periodic orbits with quantum reaction rates.

Provided an efficient computational approach for quantum reaction probabilities.

Abstract

Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this letter these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.